MSINDO

The semiempirical molecular orbital (MO) methods of quantum chemistry [1-12] are widely used in computational studies of large molecules. A number of such methods are available for calculating thermochemical properties of ground state molecules in the gas phase, including MNDO [13], MNDOC [14], MNDO/d [15-18], AMI [19], PM3 [20], SAMI [21,22], OM1 [23], OM2 [24,25] MINDO/3 [26], SINDOl [27,28], and MSINDO [29-31]. MNDO, AMI, and PM3 are widely distributed in a number of software packages, and they are probably the most popular semiempirical methods for thermochemical calculations. We shall therefore concentrate on these methods, but shall also address other NDDO-based approaches with orthogonalization corrections [23-25],... 

Due to the integral approximations used in the MNDO model, closed-shell Pauli exchange repulsions are not represented in the Hamiltonian, but are only included indirectly, e.g., through the effective atom-pair correction terms to the core-core repulsions [12], To account for Pauli repulsions more properly, the NDDO-based OM1 and OM2 methods [23-25] incorporate orthogonalization terms into the one-center or the one- and two-center one-electron matrix elements, respectively. Similar correction terms have also been used at the INDO level [27-31] and probably contribute to the success of methods such as MSINDO [29-31],... 

Stationary Point PM3 MSINDO B3LYP 6-31G UMP2 6-311G Exp. (CCSD(T)) ... 

Here L is a correction of the Mulliken approximation for the kinetic energy and All is entirely empirical and contains adjustable bond parameters. These are optimized in order to minimize the deviation from experiment for a set of reference compounds. In a way similar to INDO/S [Eq. (45)], two sets of Slater orbital exponents are used one K(0)] for intra-atomic integrals and the other (0 for molecular integrals. For comparison with experimental heats of formation, the calculated binding energies Eb [Eq. (4)] are corrected by the zero-point energies obtained from vibration analyses. Later, a substantially modified version of SINDOl, MSINDO, was developed and reparameterized for the elements H, C F, Na-Cl, Sc-Zn, and Ga-Br [63-65],... 

All semiempirical methods are parameterized for the elements H, C, N, F, and O which form the basis of most organic molecules that are of importance in pharmaceutics, biochemistry, and organic chemistry. Here it is possible to compare the statistical errors for some of the more recent methods. In Table 1, the statistics for energetic, structural, and electronic properties for first-row elements are compared for MSINDO, MNDO, AMI, and PM3. 

Another example for error statistics is given in Tables 2 and 3 for elements of the second row. Complete statistics for all second-row elements Na-Cl have so far only been published for two methods, MSINDO and MNDO/d. Both methods perform similar for the calculation of heats of formation. The agreement with experimental bond lengths seems to be slightly better with MSINDO than with MNDO/d, but as for... 

Until now, no complete error statistics has been published for third-row transition metals Sc-Zn except for MSINDO [65], MNDO/d, AMl/d, and PM3d/ PM3tm have so far only been parameterized for a small number of transition elements. 

The following subsections will present a selection of applications of the most frequently used semiempirical methods INDO/S (or ZINDO), MSINDO (or SINDOl), MNDO and MNDO/d, AMI, PM3, and SAMI and modifications of these methods... 

A possible explanation of the trends shown in Fig. 5 is that wherever high accuracy is required, semiempirical methods have recently been replaced by DFT approaches, unless they are designed for the description of certain properties (like INDO/S) or classes of materials (like MSINDO). 

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